Flagged parallel manipulators

The conditions for parallel manipulator to be flagged can be simply expressed in terms of linear dependencies between the coordinates of leg attachments, both on the base and on the platform. These dependencies permits to describe the manipulator singularities in terms of incidences between two flags (hence, the name "flagged"). Although these linear dependencies might look, at first glance, too restrictive, in this paper, the family of falgged manipulators is shown to contain large subfamilies of six-legged parallel manipulators The main interest of flagged parallel manipulators is that their singularity loci admit a well-behaved decomposition with a unique topology irrespective of the metrics of each particular design. In this paper, this topology is formallly derived and all the cells, in the configurations space of the platform, of dimension 6 (nonsingular) and dimension 5 (singular), together with their adjacencies, are worked out in detail.